Turbofan engines are typically associated with running power plants or powering airplanes. With respect to airplanes, aerodynamic instabilities such as rotating stall or surge may catastrophically lead to sudden changes in engine power or engine failure. An aeromechanical instability such as fan blade flutter may lead to fan blade breakage and loss. A precursor to flutter is characterized by a damped resonance or elastic deformation of the turbofan blades at known frequencies. The blades have natural and associated harmonic frequencies of resonance which are based on the blade structure or configuration. An axial turbomachinery blade is associated with structural mode shapes which are the natural patterns and frequencies in which the blade deflects and resonates when excited. A blade has more than one mode shape and each mode shape resonates at a particular frequency. When an instability such as stall flutter occurs, it is usually associated with one particular structural mode. It is therefore vitally important to detect precursors to aeromechanical instability in aeropropulsion compression systems in order to dampen the instability dynamics and to prevent such imminent engine instability or failure.
Precursors to aerodynamic instabilities, such as rotating stall and surge are similar to that of flutter, but do not necessarily involve a physical displacement. These instabilities are purely aerodynamic in nature, involving fluctuations in local mass flow rate and pressure throughout the compression system. Precursors to these instabilities are the damped resonances in the aerodynamics before the system crosses the threshold of instability characterized by particular frequencies.
Methods have been implemented to predict such precursors to instability. For example, U.S. Ser. No. 08/809,497, filed Apr. 7, 1996 entitled "Precursor Measurements and Stall/Surge Avoidance in Aeroengine Systems" (Docket No. EH9927 (R3952)) the disclosure which is herein incorporated by reference, describes a method of measuring an energy-type quantity of a real-valued data signal in a given frequency range and using it for compressor surge/stall avoidance. Another method generates a signal indicative of an elastic deflection or resonance of the turbofan blades at the natural frequencies associated with precursors to such aeromechanical instabilities. For example, it is known to mount strain gauges on the fan blades and use the energy of a signal generated from the strain gauge over a particular frequency interval of blade resonance associated with stall flutter as a measure of the stability of the aerocompression system with the presumption that as a structural mode of the blades approaches instability (i.e., the fan blades resonate near the frequencies associated with imminent mechanical instabilities), the resonant response of the blades to noise or external forcing will increase and hence the energy of the response near the natural frequency of the structural mode will increase.
FIGS. 1a and 1b illustrate (in exaggerated form) blade resonance or energy waves generated in a turbofan 200 having eight blades 202, 204, 206, 208, 210, 212, 214 and 216. The blades 200-216 are shown in solid form corresponding to an undeflected state, and the blades 204-208 and 212-216 are also shown in phantom form corresponding to a deflected state during a resonance or elastic deformation of the blades which may arise due to stall flutter during blade rotation. FIG. 1b maps the degree of deformation of each blade during an instant of time where the amount of blade deformation in the direction of blade rotation is a positive value and the amount of blade deformation in the direction opposite to blade rotation is a negative value.
At an instant of time during rotation of the turbofan 200 in the clockwise direction, the blade 202 is shown in FIG. 1a to have no deformation which corresponds to a deformation value of zero units for the blade 202 as mapped in FIG. 1b. The blade 204 is shown in FIG. 1a to have a slight deformation in the direction of rotation which corresponds to a positive deformation of one unit for the blade 204 as mapped in FIG. 1b. The blade 206 is shown in FIG. 1a to have an even greater deformation relative to the blade 204 in the direction of rotation which corresponds to a positive deformation of two units for the blade 206 as mapped in FIG. 1b. The blade 208 is shown in FIG. 1a to have the same deformation as the blade 204 which corresponds to a positive deformation of one unit for the blade 208 as mapped in FIG. 1b.
The blade 210 is shown in FIG. 1a to have no deformation which corresponds to a deformation value of zero units for the blade 210 as mapped in FIG. 1b. The blade 212 is shown in FIG. 1a to have a slight deformation in a direction opposite to blade rotation which corresponds to a negative deformation of one unit for the blade 212 as mapped in FIG. 1b. The blade 214 is shown in FIG. 1a to have an even greater deformation relative to the blade 212 in the direction opposite to blade rotation which corresponds to a negative deformation of two units for the blade 214 as mapped in FIG. 1b. The blade 216 is shown in FIG. 1a to have the same deformation as the blade 212 which corresponds to a negative deformation of one unit for the blade 216 as mapped in FIG. 1b. The resonance pattern shown in FIGS. 1a and 1b correspond to one cycle of deformation for each blade in the positive and negative directions for each blade rotation. However, other excitation patterns characterized by multiple cycles of resonance generated in a blade during the course of a single rotation contribute to stall flutter or other precursors to mechanical instability in aerocompression systems.
The discrete Fourier transform (DFT) is a transformation of a finite discrete time-varying sequence (or time signal), such as an AC sinusoidal waveform into its representative discrete frequency sequence (its frequency content). The frequency content may contain both positive frequencies (blade resonance in a first direction as shown by the deformed blades 204-208 in FIG. 1a) or negative frequencies (blade resonance in a direction opposite to the first direction as shown by the deformed blades 212-216 in FIG. 1a). For example, as shown in FIG. 2a, a time-varying signal A (time sequence or signal) is a superposition of two sinusoidal waveforms B and C having respective frequencies 250 Hz and 500 Hz. As shown in FIG. 2b, the corresponding frequency content (frequency sequence or signal) of the signal A which is characteristic of DFTs can be visualized as two frequency spikes 218 and 220 mapped at respective frequencies of 250 Hz and 500 Hz. Each time sequence or signal has a unique frequency sequence when transformed into a DFT and vice-versa.
The frequency content of a time-varying signal as shown in its DFT can be used to determine properties of the time sequence. For example, in the analysis of mechanical instabilities associated with turbofan blades, it is common to examine the frequency content for particular frequencies related to instability which appear before the onset of the instability. Using the frequency content of a time-varying signal to form instability precursor signals is typically much more reliable than attempting to detect instability precursors by directly processing the time signal without generating DFTs.
One method for determining instability precursors based initially on time-varying signals is by taking discrete Fourier transforms (DFTs) of data segments or portions of the time-varying signal wherein each portion spans a small predetermined interval of time, squaring the magnitude of the data segments at each discrete frequency, and then summing the squared magnitudes of the data segments over the predetermined range of frequencies associated with mechanical instabilities. This method, however, is difficult to implement because it is a burdensome task to program the DFT algorithm and apply it to sequential data sequences.
A method described in the publication "Pre-Stall Behavior of Several High-Speed Compressors", ASME Paper 94GT-387 by Tryfonidis et al. is a direct application of employing DFTs as described above. However, the method splits the positive and negative frequencies associated with rotating stall and compares them to arrive at an indication of rotating stall which appears predominantly in the positive frequency direction. The precursor signal is the energy of the positive frequencies (the sum of the squares of the positive frequency part of the DFT sequence) minus the energy of the negative frequencies (the sum of the squares of the negative frequency part of the DFT sequence).
The foregoing Tryfonidis method relates to a time-varying signal which does not change its overall repetitive characteristics over time. When analyzing a time-varying signal, which may move further or closer to its instability point or frequencies associated with rotating stall, it is necessary to perform DFTs of short time sequences at repeated time intervals to capture the time-varying nature of the signal. However, this method is inefficient to implement since it involves the full DFT analysis of a signal whenever a new data point or portion of the time signal is acquired.
In response to the foregoing, it is an object of the present invention to overcome the drawbacks and disadvantages of prior art apparatus and methods for predicting and controlling aeromechanical instabilities in turbofan engines.